Management Science is an interdisciplinary field that employs and integrates methods of applied mathematics, economics, and statistics to help decision making in the management context. Together with the ever increasing availability of computational resources, the efficient use of quantitative methods of management science has become a vital instrument to achieve competitive advantage. For instance, efficient scheduling of flights between the many ports spread all over the world is facilitated by a combination of advanced mathematical and computational tools. In this module, we focus on the methods of mathematical programming that express decision making problems as optimisation problems where quantities of interest, such as profit and cost, are maximised or minimised, satisfying organisational constraints. This module will provide the student with a deep understanding of standard optimisation models and techniques and will show how they can be used to identify and solve problems encountered by managers in practice. It will provide the student with skills to formulate organisational problems in the language of mathematics, select suitable techniques to solve them, and use specialised software programs to carry out these tasks in practice.